NAME:ŞERİFE

SURNAME: ÖZDER

STUDENT NUMBER: 20110661

SUBJECT:HİSTORY OF MATHEMATİCS

CONTAİNS

1) Prehistoric Mathematics

2) Babylorian Mathematics

3) Egyption Mathematics

4) Gareek Mathematics

5) Chinese Mthematics

6) Indian Mathematics

7) Islanic Mathematics

8)Medieval Mathematics

9) Renaissance Mathematics

10)Modern Mathematics

11) Reference

PREHİSTORİC MATHEMATİCS

The origins of mathematical thought lie in the concepts of number,

magnitude, and form. Modern studies of animal cognition have shown that

these concepts are not unique to humans. Such concepts would have been

part of everyday life in hunter-gatherer societies. The idea of the "number"

concept evolving gradually over time is supported by the existence of

languages which preserve the distinction between "one", "two", and "many",

but not of numbers larger than two

The oldest known possibly mathematical object is the Lebombo bone,

discovered in the Lebombo mountains of Swaziland and dated to

approximately 35,000 BC. It consists of 29 distinct notches cut into a

baboon's fibula. Also prehistoric artifacts discovered in Africa and

PREHISTORIC

France, dated between 35,000 and 20,000 years old, suggest early attempts to quantify timeThe Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be as much as 20,000 years old and consists of a series of tally marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either the earliest known demonstration of sequences of prime numbers or a six month lunar calendar. In the book How Mathematics Happened: The First 50,000 Years, Peter Rudman argues that the development of the concept of prime numbers could only have come about after the concept of division, which he dates to after 10,000 BC, with prime numbers probably not being understood until about 500 BC. He also writes that "no attempt has been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and some numbers that are almost multiples of 10”

PREHISTORIC

Predynastic Egyptians of the 5th millennium BC pictorially represented

geometric designs. It has been claimed that megalithic monuments in

England and Scotland, dating from the 3rd millennium BC, incorporate

geometric ideas such as circles, ellipses, and Pythagorean triples in their

design

All of the above are disputed however, and the currently oldest undisputed

mathematical usage is in Babylonian and dynastic Egyptian sources. Thus it

took human beings at least 45,000 years from the attainment of behavioral

modernity and language (generally thought to be a long time before that) to

develop mathematics as such.

BABYLONIAN MATHEMATICS

Babylonian mathematics refers to any mathematics of the people of

Mesopotamia (modern Iraq) from the days of the early Sumerians through the

Hellenistic period almost to the dawn of Christianity.] It is named Babylonian

mathematics due to the central role of Babylon as a place of study. Later under

the Arab Empire, Mesopotamia, especially Baghdad, once again became an

important center of study for Islamic mathematics.

BABYLONIAN

In contrast to the sparsity of sources in Egyptian mathematics, our knowledge of

Babylonian mathematics is derived from more than 400 clay tablets unearthed

since the 1850s. Written in Cuneiform script, tablets were inscribed whilst the

clay was moist, and baked hard in an oven or by the heat of the sun. Some of

these appear to be graded homework.

The earliest evidence of written mathematics dates back to the ancient

Sumerians, who built the earliest civilization in Mesopotamia. They developed a

complex system of metrology from 3000 BC. From around 2500 BC onwards,

the Sumerians wrote multiplication tables on clay tablets and dealt with

geometrical exercises and division problems. The earliest traces of the

Babylonian numerals also date back to this period

BABYLONIAN

Babylonian mathematics were written using a sexagesimal (base-60) numeral

system. From this derives the modern day usage of 60 seconds in a minute, 60

minutes in an hour, and 360 (60 x 6) degrees in a circle, as well as the use of

seconds and minutes of arc to denote fractions of a degree. Babylonian

advances in mathematics were facilitated by the fact that 60 has many divisors.

Also, unlike the Egyptians, Greeks, and Romans, the Babylonians had a true

place-value system, where digits written in the left column represented larger

values, much as in the decimal system. They lacked, however, an equivalent of

the decimal point, and so the place value of a symbol often had to be inferred

from the context.

EGYPTIAN MATHEMATICS

Image of Problem 14 from the Moscow Mathematical Papyrus. The problem

includes a diagram indicating the dimensions of the truncated pyramid.

Egyptian mathematics refers to mathematics written in the Egyptian language.

From the Hellenistic period, Greek replaced Egyptian as the written language of

Egyptian scholars.

EGYPTIAN

The most extensive Egyptian mathematical text is the Rhind papyrus

(sometimes also called the Ahmes Papyrus after its author), dated to c. 1650 BC

but likely a copy of an older document from the Middle Kingdom of about 2000-

1800 BC. It is an instruction manual for students in arithmetic and geometry. In

addition to giving area formulas and methods for multiplication, division and

working with unit fractions, it also contains evidence of other mathematical

knowledge, including composite and prime numbers; arithmetic, geometric and

harmonic means; and simplistic understandings of both the Sieve of

Eratosthenes and perfect number theory (namely, that of the number 6)It also

shows how to solve first order linear equations as well as arithmetic and

geometric series

GREEK MATHEMATICS

The Pythagorean theorem. The Pythagoreans are generally credited with the

first proof of the theorem.

Greek mathematics refers to the mathematics written in the Greek language

from the time of Thales of Miletus (~600 BC) to the closure of the Academy of

Athens in 529 AD. Greek mathematicians lived in cities spread over the entire

Eastern Mediterranean, from Italy to North Africa, but were united by culture and

language. Greek mathematics of the period following Alexander the Great is

sometimes called Hellenistic mathematics

GREEK

Greek mathematics was much more sophisticated than the mathematics that

had been developed by earlier cultures. All surviving records of pre-Greek

mathematics show the use of inductive reasoning, that is, repeated observations

used to establish rules of thumb. Greek mathematicians, by contrast, used

deductive reasoning. The Greeks used logic to derive conclusions from

definitions and axioms, and used mathematical rigor to prove them

Greek mathematics is thought to have begun with Thales of Miletus (c. 624–

c.546 BC) and Pythagoras of Samos (c. 582–c. 507 BC). Although the extent of

the influence is disputed, they were probably inspired by Egyptian and

Babylonian mathematics. According to legend, Pythagoras traveled to Egypt to

learn mathematics, geometry, and astronomy from Egyptian priests.

GREEK

Eudoxus (408–c.355 BC) developed the method of exhaustion, a precursor of

modern integration and a theory of ratios that avoided the problem of

incommensurable magnitudes,The former allowed the calculations of areas and

volumes of curvilinear figures, while the latter enabled subsequent geometers to

make significant advances in geometry. Though he made no specific technical

mathematical discoveries, Aristotle (384—c.322 BC) contributed significantly to

the development of mathematics by laying the foundations of logic

CHINESE MATHEMATICS

The Nine Chapters on the Mathematical Art, one of the earliest surviving

mathematical texts from China (2nd century AD).

Early Chinese mathematics is so different from that of other parts of the

world that it is reasonable to assume independent development. The

oldest extant mathematical text from China is the Chou Pei Suan Ching,

variously dated to between 1200 BC and 100 BC, though a date of about

300 BC appears reasonable

CHINESE

Of particular note is the use in Chinese mathematics of a decimal positional

notation system, the so-called "rod numerals" in which distinct ciphers were

used for numbers between 1 and 10, and additional ciphers for powers of ten

Thus, the number 123 would be written using the symbol for "1", followed by the

symbol for "100", then the symbol for "2" followed by the symbol for "10",

followed by the symbol for "3". This was the most advanced number system in

the world at the time, apparently in use several centuries before the common era

and well before the development of the Indian numeral system. Rod numerals

allowed the representation of numbers as large as desired and allowed

calculations to be carried out on the suan pan, or Chinese abacus. The date of

the invention of the suan pan is not certain, but the earliest written mention dates

from AD 190, in Xu Yue's Supplementary Notes on the Art of Figures.

INDIAN MATHEMATICS

Main article: Indian mathematics

See also: History of the Hindu-Arabic numeral system

The numerals used in the Bakhshali manuscript, dated between the 2nd century

BCE and the 2nd century CE.

The earliest civilization on the Indian subcontinent is the Indus Valley Civilization

that flourished between 2600 and 1900 BC in the Indus river basin. Their cities

were laid out with geometric regularity, but no known mathematical documents

survive from this civilization

ISLAMIC MATHEMATICS

The Islamic Empire established across Persia, the Middle East, Central Asia,

North Africa, Iberia, and in parts of India in the 8th century made significant

contributions towards mathematics. Although most Islamic texts on mathematics

were written in Arabic, most of them were not written by Arabs, since much like

the status of Greek in the Hellenistic world, Arabic was used as the written

language of non-Arab scholars throughout the Islamic world at the time.

Persians contributed to the world of Mathematics alongside Arabs.

MEDIEVAL EUROPEAN MATHEMATICS

Medieval European interest in mathematics was driven by concerns quite

different from those of modern mathematicians. One driving element was the

belief that mathematics provided the key to understanding the created order of

nature, frequently justified by Plato's Timaeus and the biblical passage (in the

Book of Wisdom) that God had ordered all things in measure, and number, and

weight.

Boethius provided a place for mathematics in the curriculum in the 6th century

when he coined the term quadrivium to describe the study of arithmetic,

geometry, astronomy, and music. He wrote De institutione arithmetica, a free

translation from the Greek of Nicomachus's Introduction to Arithmetic; De

institutione musica, also derived from Greek sources; and a series of excerpts

from Euclid's Elements. His works were theoretical, rather than practical, and

were the basis of mathematical study until the recovery of Greek and Arabic

mathematical works.

RENAISSANCE MATHEMATICS

During the Renaissance, the development of mathematics and of accounting

were intertwined. While there is no direct relationship between algebra and

accounting, the teaching of the subjects and the books published often intended

for the children of merchants who were sent to reckoning schools (in Flanders

and Germany) or abacus schools (known as abbaco in Italy), where they learned

the skills useful for trade and commerce. There is probably no need for algebra

in performing bookkeeping operations, but for complex bartering operations or

the calculation of compound interest, a basic knowledge of arithmetic was

mandatory and knowledge of algebra was very useful.

MODERN MATHEMATICS

This century saw the development of the two forms of non-Euclidean geometry,

where the parallel postulate of Euclidean geometry no longer holds. The

Russian mathematician Nikolai Ivanovich Lobachevsky and his rival, the

Hungarian mathematician János Bolyai, independently defined and studied

hyperbolic geometry, where uniqueness of parallels no longer holds. In this

geometry the sum of angles in a triangle add up to less than 180°. Elliptic

geometry was developed later in the 19th century by the German mathematician

Bernhard Riemann; here no parallel can be found and the angles in a triangle

add up to more than 180°. Riemann also developed Riemannian geometry,

which unifies and vastly generalizes the three types of geometry, and he defined

the concept of a manifold, which generalizes the ideas of curves and surfaces.

REFERENCE

http://en.wikipedia.org/wiki/History_of_mathematics